Last night I had about 2 hours so I managed to get the feet sorted out. I bought some rubber feet from Home Depot for about $2 that I thought would be perfect.
However, I left a 1/4" lip all the way around the side panels of the cabinet where the interior panels connect. The bottom panel was actually elevated 1/4" when the cabinet was supported by the side panels. These feet weren't quite tall enough so I made some spacers out of MDF. I made them smaller than the rubber feet because I did not want them to be seen at all. I'm not 100% sure this was the best solution but no one will ever see it so who cares... OK, I do but I can't think of a better solution.
In order to locate the feet, I used 2 pencils that my daughter left out as spacers from the edges. They were literally just sitting in front of me so I went for it. Normally, something like this would slow me down for hours while I researched where other people placed their cabinet feet and what they used, etc. but I'm trying to get past that mental hurdle.
Once I located all 4 feet, I used an awl to mark the center point for my drill and I drilled out the holes.
Then I attached the feet using the spacers I made. I didn't even paint the spacers and it is bothering me just thinking about it but that seems like a waste of time. Ideally, I'd have been able to use some 1/2" black PVC piping and make 4 spacers of it if such a thing even exists... hmm... looks like i'm headed to Home Depot at lunch today. Again. I can't let this go.
It looks good and the final result lifts the cabinet off the ground perfectly - There will be room for the t-molding along the bottom edge of the side panels and the cabinet will still be spaced off of the ground nicely.
Next up tonight is to get the access door installed along with the magnets for the control panel. I tried yesterday but as I feared it was now too tight due to the paint. Nothing a little sanding can't fix but it will probably take me an hour or so to get it just right.
EDIT: I swapped out the MDF spacers for spacers made out of PVC pipe and sprayed black. Scroll down to see what I did to fix this abomination.